Heavenly equations in de Sitter space

We demonstrate that all anti-self-dual Einstein metrics with non–zero cosmological constant $\mathrm{\Lambda }$ locally arise from solutions of a single second order PDE introduced by Lipstein and Nagy. We show how this equation fits into the hyper–heavenly formalism of Plebański, and establish a Lax pair. Finally we show how Plebański’s second heavenly equation arises in the limit as $\mathrm{\Lambda }\to 0$.